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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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Square Roots

To square a number, we raise the number to the second power.

For example, 62 = 36.

To find the square root of a number, we reverse the squaring process.

For example,

â€¢ one square root of 36 is 6, because 62 = 36;

â€¢ another square root of 36 is -6, because (-6)2 = 36.

Each positive real number has a positive square root and a negative square root.

The positive square root is called the principal square root.

The radical symbol, , is used to denote the principal square root of a number.

For example, the principal square root of 36 is written like this:

Since the principle square root is the positive square root, we have:

A radical is the part of an expression that consists of a radical symbol and a radicand.

A negative number, for example -36, does not have square roots that are real numbers. Thatâ€™s because a real number times itself always gives a nonnegative number.

 62 = 36 (-6)2 = +36

Definition â€” Square Root

For a nonnegative real number, a, the principal square root of a is written .

If b is a nonnegative real number and b2 = a, then

Example:

because b is nonnegative and 62 = 36.

When you square the square root of a nonnegative number, the result is the original number.

For example,

Likewise, when you take the square root of a nonnegative number squared, the result is the original number.

For example,